This is an oak tree of my neighbors. Two yrs ago I had a tree crash into this one and it leaned on this one for at least 2 months. It was perfectly fine before this so I didn't know if my tree somehow injured it or not.

Actually, no. That article is incorrect, technically speaking. Suckers originate from below the soil surface, water sprouts from above. Both are from adventitious buds, so are not well anchored to the rest of the tree. Water sprouts especially, will have a greater tendency to break off in storms.

For some trees, water sprouts and especially suckers are normal in their life. But no matter what the plant, they will be encouraged by tissue damage or plant stresses. This is another reason why pruning with correctly sized and sharp pruning tools is so important. While the end result of even correct pruning is positive, it still damages the tree. But a smooth, clean cut done correctly is far less damaging than a ratted cut, or just being broken off.

There are a few "stop suckers" chemical treatments on the market, but I don't know how they work or even if they work, so I can't comment.

Years ago I was taught that overly-heavy pruning, especially in spring or summer, encourages epicormic growth. That certainly appeared to be the case with an ornamental crabapple that was "pruned" locally, it responded by sending out a large number of watersprouts. From what I've read it likely has to do with changes in the level of light, such as from this type of heavy pruning, or a nearby tree falling down and letting in more light.

It looks like in the picture of the oak there is also a vertical crack in the trunk in the area of the watersprouts??

Typically we think of frost cracks or sunscald when the crack is on the south or south-west side. Whether that's the case here I wouldn't know and I'm a generalist not an arborist. I read an interesting article a while back that suggests frost cracks and sunscald may not be quite what they seem to be (the PDF jumps a bit between pages so one has to scroll past an intervening article to read the whole thing:

Sue, the Wisconsin DNR link was very enlightening, since it goes beyond the basic "what is" answer for frost cracks and sunscald. Thanks!

It's unlikely that the crack you show, Kabby, is a frost crack. The physical force that causes frost cracks would have pulled the bark much farther apart. More likely it is caused by some defect or infection under the bark and the normal pull/pressure forces present in any tree. (That's why the crack has not widened.)

Chelle, I don't want to poo poo your effort to find possible explanations: few people take the time, or even know how to think outside the box (or even inside the box, for that matter). You deserve kudos for that. However, I am going to shoot down your shading theory of the epicormic growth.

Bark that is that old and thick would be sufficient protection from frost cracking on its own. Even if one were to assign an intelligence to the tee to "hurry up and protect the trunk with shade", an evolutionary path to back up such a theory is lacking. And it probably doesn't get that cold in Alabama, anyway(?). More likely, the sudden difference in light trigger adventitious growth from under the bark layer, and/or possibly some other stress as mentioned earlier. The rush of growth, relative to the canopy growth is due to the presence of several factors, including the convergence of optimal conditions: lots of light with a relatively protected and more favorable environment, an unlimited supply of water and nutrients and the faster, vigorous growth that comes with the juvenile growth that they are. (Normal canopy growth is always mature growth.)
But Chelle, if sunscald were a possibility (on thin bark) then your shading theory could have merit.